1. Theorems Relating Lines and Planes

2. Review From Yesterday - Answer: ONE line is formed
What is the difference between collinear points and coplanar lines?
What happens when two planes intersect?
What are the 4 ways you can create a plane?
Answer: collinear points are points on the same line and coplanar lines are lines in the same plane
- Answer: ONE line is formed
- Answer: 3 noncollinear points, a line and a point off
the line, two intersecting lines, two parallel lines

3. Theorem 1
If a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them.

4. Theorem 2
Through a given point there passes one and only one plane perpendicular to a given line.

5. Theorem 3
Through a given point there passes one and only one line perpendicular to a given plane.

6. Theorem 4
If two planes are perpendicular to the same line, they are parallel.

7. Let’s work on Some Questions
A line perpendicular to a plane is perpendicular to every line in the plane. True of False?
Answer: False
• Through a point outside a plane, one
and only one plane can be drawn
perpendicular to the plane. True or False?
Answer: False

8. More Practice!
Fill in the blank: Two planes that are perpendicular to the same line are _____________ to each other
Answer: parallel
Two lines _____________ to the same plane are parallel.
Answer: Perpendicular

9. 3 4 4

10. 2 4

11. (2) Planes P and R are parallel.
1. Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P and R?
(2) Planes P and R are parallel.
Lines and intersect at point E. Line m is perpendicular to lines and
at point E.
Which statement is always true?
(3) Line m is perpendicular to the plane

12. 3. For this rectangular solid, Planes EGH and GAB intersect to form line
4. One dihedral angle formed by planes l and q is:
P – YZ – A

13. 5. If lines n and m are each perpendicular to plane A, what is the relationship between n and m ?
n and m are coplanar
6. What happens when two planes intersect? ________________________________
One line is formed